|Speaker||Il Woo Cho|
|Dept.||St. Ambrose University, USA|
In this talk, we discuss algebra, analysis, representation theory, operator algebra theory, and free probability on scaled-hypercomplex systems which was recently introduced. Here, hypercomplex structures are roughly understood to be certain algebraic structures of tuples, or pairs of complex numbers equipped with suitable binary operations. Well-known quaternions and split-quaternions form hypercomplex structures. In this talk, we generalize such structures up to scales of real numbers. For example, if a fixed scale is -1, then one has the quaternions, meanwhile, if a scale is 1, then we have the split-quaternions.